The Six Principles of the Principles and Standards for School Mathematics
Curriculum: what is meant by a comprehensive curriculum: doesn’t the selected textbook pretty much define the mathematics curriculum that is to be presented?
A comprehensive curriculum involves building knowledge based upon a previous foundation for further use. We agreed that a comprehensive curriculum and a textbook are not the same thing; however, the textbook can be utilized as a tool within the curriculum.
Teaching: how do the following terms relate to effective teaching: reflection, sense making, promoting autonomy, and discourse?
As a part of effective teaching, both the teacher and the students need to be able to reflect on their work and experiences in the classroom in order to grow in their understanding.
Sense making is the ability to transfer knowledge in a way that students can comprehend. This could involve multiple approaches and adapting based on the students.
As effective teachers, we hope to promote autonomy; it is essential that students become independent and confident in their mathematical abilities rather than relying solely on the teacher.
Discourse is important to effective teaching because it creates an environment of open interaction and communication between all individuals in the classroom.
Learning: “Students’ ability to provide correct answers is not always an indicator of a high level of conceptual understanding.” Your comments? How do you promote “active engagement” of your students?
Students must develop an understanding of HOW a solution came to be rather than just knowing the answer. This allows them to deepen and connect their knowledge. With the teacher tailoring their lesson plan to the students in the class, we can emphasize the process and keep it fresh and interesting.
Assessment Principle Provide 3 key points from the Assessment principle. Respond to: “The sole purpose of assessment is to measure student achievement and to assign grades.”
A focus of assessment should be on whether or not a student understands the material. Assessment is also for the teacher to judge whether or not a topic has been received well by the class and to see if the teacher is explaining material properly. After evaluating themselves, the teachers should then be using the information that they gained from the assessment to improve their teaching technique for future classes. The primary goal of assessment should not be to assign a grade, but to measure student success. The key points outlined in the NCTM standards are: Assessments should:
reflect the mathematics that students should know and be able to do;
enhance mathematics learning;
promote equity;
be an open process;
promote valid inference;
be a coherent process.
We agree with these points because they promote the benefits of actual learning for the student rather than memorizing an algorithm for a grade. Teachers that give assessments solely to assign grades disadvantage their students because the students will become focused on grades over learning.
Equity Principle Provide 3 key points from the Equity principle Respond to: What are your experiences/opinions with regard to “tracking” in mathematics?
1. high expectations for student’s learning 2. promoting reasonable accommodations to support learning 3. differences and needs must be accepted and met
Tracking in mathematics allows the student body to be divided into “higher”, “lower”, and “regular” tracks of courses/classes. This allows teachers and students to work at a pace that better fits their learning abilities. We believe that within certain tracks there is equality among students, but they look differently at the others outside of their class.
Tracks can have a negative affect on students as well. Students are placed in tracks and moving from one track to another can be difficult. Track placement is not a perfect science, it is subject to flaws. Some students may be placed in a track that they do not belong in, for instance if a student is placed in the remedial course yet belongs in the higher end math class this student may become bored and be a distraction to the rest of the students. Technology Principle Provide 3 key points from the Technology principle. Respond to: What do you feel are “appropriate” uses of technology? Give 3 examples and 2 non-examples of “appropriate” uses.
3 Key Points: Technology enhances learning: provides more in-depth understanding and from multiple perspectives Technology supports effective mathematics teaching: teachers can use simulations Technology influences what type of mathematics is taught Appropriate Uses: Calculator to check your answers Document Camera- to put book under camera and point to specific concepts in a problem Computer programs- to plot points, create geometric shapes Adapt lessons for students with special needs
Non-examples: Online textbooks: The are not always accessible Text messaging: More distraction than help
Curriculum:
what is meant by a comprehensive curriculum: doesn’t the selected textbook pretty much define the mathematics curriculum that is to be presented?
A comprehensive curriculum involves building knowledge based upon a previous foundation for further use.
We agreed that a comprehensive curriculum and a textbook are not the same thing; however, the textbook can be utilized as a tool within the curriculum.
Teaching:
how do the following terms relate to effective teaching: reflection, sense making, promoting autonomy, and discourse?
As a part of effective teaching, both the teacher and the students need to be able to reflect on their work and experiences in the classroom in order to grow in their understanding.
Sense making is the ability to transfer knowledge in a way that students can comprehend. This could involve multiple approaches and adapting based on the students.
As effective teachers, we hope to promote autonomy; it is essential that students become independent and confident in their mathematical abilities rather than relying solely on the teacher.
Discourse is important to effective teaching because it creates an environment of open interaction and communication between all individuals in the classroom.
Learning:
“Students’ ability to provide correct answers is not always an indicator of a high level of conceptual understanding.”
Your comments? How do you promote “active engagement” of your students?
Students must develop an understanding of HOW a solution came to be rather than just knowing the answer. This allows them to deepen and connect their knowledge. With the teacher tailoring their lesson plan to the students in the class, we can emphasize the process and keep it fresh and interesting.
Assessment Principle
Provide 3 key points from the Assessment principle.
Respond to: “The sole purpose of assessment is to measure student achievement and to assign grades.”
A focus of assessment should be on whether or not a student understands the material. Assessment is also for the teacher to judge whether or not a topic has been received well by the class and to see if the teacher is explaining material properly. After evaluating themselves, the teachers should then be using the information that they gained from the assessment to improve their teaching technique for future classes. The primary goal of assessment should not be to assign a grade, but to measure student success.
The key points outlined in the NCTM standards are:
Assessments should:
We agree with these points because they promote the benefits of actual learning for the student rather than memorizing an algorithm for a grade. Teachers that give assessments solely to assign grades disadvantage their students because the students will become focused on grades over learning.
Equity Principle
Provide 3 key points from the Equity principle
Respond to: What are your experiences/opinions with regard to “tracking” in mathematics?
1. high expectations for student’s learning
2. promoting reasonable accommodations to support learning
3. differences and needs must be accepted and met
Tracking in mathematics allows the student body to be divided into “higher”, “lower”, and “regular” tracks of courses/classes. This allows teachers and students to work at a pace that better fits their learning abilities. We believe that within certain tracks there is equality among students, but they look differently at the others outside of their class.
Tracks can have a negative affect on students as well. Students are placed in tracks and moving from one track to another can be difficult. Track placement is not a perfect science, it is subject to flaws. Some students may be placed in a track that they do not belong in, for instance if a student is placed in the remedial course yet belongs in the higher end math class this student may become bored and be a distraction to the rest of the students.
Technology Principle
Provide 3 key points from the Technology principle.
Respond to: What do you feel are “appropriate” uses of technology? Give 3 examples and 2 non-examples of “appropriate” uses.
3 Key Points:
Technology enhances learning: provides more in-depth understanding and from multiple perspectives
Technology supports effective mathematics teaching: teachers can use simulations
Technology influences what type of mathematics is taught
Appropriate Uses:
Calculator to check your answers
Document Camera- to put book under camera and point to specific concepts in a problem
Computer programs- to plot points, create geometric shapes
Adapt lessons for students with special needs
Non-examples:
Online textbooks: The are not always accessible
Text messaging: More distraction than help